I have ran 2S LiPo on many of my brushed cars without LVC built into the ESC... although an LVA is preferred as mentioned above, I never used one and was careful to stop running the car at the first hint of battery fade, never over discharged a battery being careful. Not uncommon for many racers to disable LVC as well to get an extra lap in a long main today.
I found it necessary to gear down because LiPo tends to provide more punch and this wasn't an issue for the ESC, but longer run times from LiPo would tend to build up heat on the motor and wear out the motors faster, more info here:
I don't see any reason to use NiMh anymore, there are too many reasons why LiPo is better.
Good Luck!